Medidas Exteriores

Dynamic fluctuations in the protein conformation are important in regulating protein function, and mutations can alter the dynamics [214, 215]. The correlation coefficients of the atomic fluctuations were analyzed for each residue over time in order to identify the correlated motions and the change between wild-type PRMD and PR20MD simulations. Dynamical cross-correlation maps (DCCM) were drawn for each simulation (Figure 4-7). Correlation coefficients of higher than 0.25 or lower than -0.25 are shown in the maps [211], and peaks identified for correlated motions are labeled in the maps. The peaks of correlated motions identified in the MD simulations of wild type PR and PR20 (Figure 4-7 a and Figure 4-7 b) are notably larger than for the corresponding simulations of the inactive D25N mutants (Figure 4-7 c and Figure 4-7 d). Our MD simulations agree with the NMR study showing that the single mutation of D25N altered the dynamic properties of the PR [179]. However, introducing the D25N mutation had no significant effect on the atomic positions or hydrogen bond interactions when comparing the PRWT and PRWTD25N dimers [179].

Correlated motions identified in quadrants I and III of DCCM represent intra-subunit relationships and are consistent with previous MD simulations [216, 217].The secondary structure patterns and the interface contacts have mainly positive correlations within each monomer, while anti-correlations exist between these regions. The peaks of correlated motions observed in the two monomers are similar but

Figure 4-7 Dynamic Cross Correlation Maps show correlated motions of:

(A) PRWTMD, (B) PR20MD, (C) PRWTD25NMD and (D) PR20D25NMD. Cross-correlation coefficients Cij

larger than 0.25 and smaller than -0.25 are shown in maps with the intensity represented as follows: red squares 0.25 <Cij< 1, blue squares -1 <Cij< -0.25. The four quadrants are labeled. Quadrants I and II show

intra-subunit correlated motions. Quadrant II and the symmetry related quadrant IV show inter-subunit correlated motions. Peaks of positive correlated correlation are labeled with numbers for each monomer (quadrant I and III), and groups of peaks are labeled with letters in quadrant II.

have different intensities, suggesting that each monomer has a similar pattern of dynamic motions. Correlated inter-subunit motions were identified in quadrants II and IV of DCCM.Anti-correlations are mostly seen in the inter-subunit quadrants, showing that motions between two monomers have opposing directions.Correlated motions of the flaps with the active site cavity and peripheral residues have been reported in different MD simulations of wild-type PR [217, 218]. When the DCCMs are compared for the four MD simulations, the correlation coefficients in the inter-subunit quadrant are generally weaker in PR20MD and PR20D25NMD than in PRWTMD and PRWTD25NMD. The anti-correlated motions of the flaps

(residues 45-48 and 53-58) in the inter-subunit quadrant are weaker or disappear in PR20MD and

PR20D25NMD, respectively. These motions suggest that the two flaps tend to fluctuate more independently

in the PR20 mutant than in the wild-type enzyme. In summary, correlated motions are well preserved in

each monomer, however, the cross communications between the two monomers are impaired in PR20

relative to wild type PR dimers.

4.4 Discussion

The variant PR20 from a clinical isolate is highly resistant to the tested clinical inhibitors, which

show several orders of magnitude worse affinity for PR20 compared to the wild type enzyme. Moreover,

in contrast to the wild type precursor, saquinavir and darunavir do not inhibit autoprocessing of the precursor comprising TFR-PR20. Previous crystallographic studies of the PR20 dimer showed a large

variation in the conformation of the flaps in the ligand-free structures. Here, we report two new conformations, designated twisted and tucked flap, observed in the dimer of PR20D25N. Formerly, three

highly drug resistant variants PRP51, MDR769 and PR20 were observed to have widely separated flaps in

their dimer structures, suggesting a common mechanism for resistance to inhibitors [105, 107, 201], and new inhibitors have been designed to target the wide open flaps[219]. Among the new structures reported here, PR20D25Ntwist has the highest separation of the flap tips in the dimer.The rotation of the

PR20D25Ntuck exhibits a unique flap conformation, which has not been described previously for crystal

structures of HIV protease. The tucked flap enters the active site cavity, and this conformation prevents the binding of substrates or inhibitors. Again, this tucked flap provides a novel mechanism to lower the affinity for inhibitors.

The conformational dynamics of proteins contributes to their biological function, and correlated motions of domains regulate biological function [220, 221]. In the PR dimer, the substrate binding cavity is constructed by two identical monomers, and the cooperative opening and reclosing of the two flaps is critical during proteolysis of the natural substrate and binding of an inhibitor. The flaps exhibit diverse conformations in the crystal structures of ligand-free PR20 [201]. The new crystal structures reported here for ligand-free dimers of PR20D25N show additional conformational variation, including an unusual tucked

form, where one flap is tucked inside the active site cavity. Cluster analysis of our MD simulations for PR20

and wild type PR shows that the mutations influence the conformational dynamics of the flaps. Isothermal titration calorimetry shows that mutations in PR20 increase the stability of the monomer compared to wild

type PR [200].In the MD simulations, the individual monomers in the PR20 and wild type enzyme dimers

exhibit similar conformational dynamics. However, the correlated motions between the two subunits of the dimer differ in the PR20 mutant and wild type enzyme. PR20 lacks correlated motions between the flap

and the other subunit in the dimer, which will tend to destabilize the flaps, consistent with the diverse conformations observed in crystal structures of this mutant.

In summary, subtle rearrangements in the conformational ensemble of the flaps induced by the mutations impair the dynamics, and consequently the proteolytic activity and inhibitor affinity of the mutant enzyme. These changes in dynamics will contribute to the high level resistance of PR20. Importantly, the discovery of new flap conformations in crystal structures and MD simulations may hint at designs for novel antiviral inhibitors that capture the variant flap conformations of the resistant mutants.

4.5 Acknowledgment

Data were collected at Southeast Regional Collaborative Access Team (SER-CAT) beamline 22ID at the Advanced Photon Source, Argonne National Laboratory. Supporting institutions may be found at http://www.ser-cat.org/members.html. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract W-31-109-Eng- 38.

A HYBRID IMPLEMENTATION OF PARALLEL AMORTIZED FAST MULTIPOLE ALGORITHM FOR THE

MOLECULAR MODELING PROGRAM: AMMP

(In-preparation: Chen-Hsiang Shen and Robert W. Harrison)

5.1 Abstract

Molecular dynamics simulation is a tool used to study the molecular basis of chemical and biological problems. The efficient calculation on electrostatic and long range forces, which is the (N2₎

summation by naive algorithm, is the central problem on using molecular dynamics simulation. An OpenMP-CUDA implementation of parallel molecular dynamic program, AMMP, is presented for protein simulation. The hybrid implementation provides high efficiency of molecular dynamic simulation. The new parallel implementation of AMMP is capable of simulating molecular systems with more than half million atoms with excellent acceleration and parallel efficiency. The combination of OpenMP-CUDA can accelerate the simulation about 20 fold faster than the 8-threaded CPU based AMMP.

5.2 Introduction

Molecular dynamics simulation is a powerful computational tool for modeling the behavior of proteins and protein-ligand complexes. In the classical limit, molecular dynamics finds a numerical solution for the motion of the molecules in a molecular mechanics potential or force-field. A molecular mechanics potential can be divided in terms of its computational complexity into two sorts of terms: covalent geometry terms that define covalent chemical bonds, angles, torsional effects and chirality and non-bonded terms like van der Waals and electrostatic terms. The number of covalent geometry terms scales asymptotically as O(N) where N is the number of atoms, while the number of non-bonded terms scales as the number of unique pairs of atoms or O(N2_).

The naïve way to calculate non-bonded terms is to loop over each pair of atoms. Therefore significant effort has been spent on accelerating the calculations for the non-bonded terms. One of the first

approximations was to use a cutoff radius, which converts the non-bonded calculations to O(N). However, this approximation violates the conservation of energy and momentum with predictably dire consequences [110, 111, 118]. Recent work has focused developing algorithms that can calculate the non- bonded terms without using an explicit loop over all the pairs of atoms. Two general classes of algorithms are used for this, the Ewald method which uses a Fourier transform[112] and the Fast Multipole Method (FMM) which uses power series expansion and tree based data structure[113, 222]. This paper describes accelerating the implementation of the FMM used in the program AMMP on multi-core and GPU architectures [118, 223].

Even though both the Ewald and FMM methods are effective at speeding up the calculation of the long-range terms, the calculation is still expensive. Further economies are possible by using an Amortization algorithm [118, 223], where a small amount of additional effort translates into significant savings. Amortization is an example of a Multi-Time step algorithm [224]. The force fields used in molecular dynamics are split as fast evolving short-range terms and slow moving long-range terms. Energy terms that evolve quickly in time, namely the covalent geometry terms and non-bonded interactions between nearby atoms are explicitly treated on a fast time scale. Energy terms that evolve more slowly are treated with a slow time scale. The key difference between a classical multi-time step algorithm and an amortized algorithm is that the amortized algorithm maintains a local expansion of the forces and energies which it updates when the atoms have moved sufficiently and the multi-time step expansion simply updates the long-range terms less frequently than the covalent and local non-bonded terms. The advantage of using an update that depends on the distance the atoms have moved is that it automatically adapts the update frequency to the speed of the atoms.